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Template:Norm/doc
The {{norm}} mathematical formatting template and/or mathematical function template gives an HTML+CSS or a LaTeX formatted norm of a mathematical expression and/or the numerical result of the norm of the expression.
Contents
Usage
- {{norm|expression|format}}
or
- {{norm|expression|degree|format}}
or
- {{norm|expression yielding a numerical n-vector, n in {1, 2, 3, 4}|#}}
or
- {{norm|expression yielding a numerical n-vector, n in {1, 2, 3, 4}|degree|#}}
where
- the first argument is a mathematical expression;
- the second argument is the degree
of the norm (defaultp, p ≥ 1,
, i.e. Euclidean norm);2
and the last (either second or third) argument is one of
- htm: HTML+CSS [single line] markup (default),
- HTM: HTML+CSS [multiline] markup,
- tex: LaTeX [single line] markup,
- TEX: LaTeX [multiline] markup,
- #: numerical result.
As an alternative to using LaTeX rendered PNG images (tex
or TEX
options), the htm
or HTM
options will produce an HTML+CSS formatted expression. (Do not use this option inside <math>...</math> tags.)
NOTE: To get rendered LaTeX, you must use the {{math}} template (or {{#tag:math|...}}, although you should use the {{math}} template for consistent formatting, e.g. font face and font size), since you cannot evaluate templates, parser functions or magic words inside <math>...</math> tags.
Valid input
A mathematical expression. If the numerical result is wanted, the expression must yield an [unformatted] numericaln |
n ∈ {1, 2, 3, 4} |
Examples
Code Result {{math| {{norm}} |&}} || · ||{{math| {{norm|htm}} |&}} || · ||{{math| {{norm|tex}} |$}} {{math| {{norm|''x''}} |&}} || x ||{{math| {{norm|''x''|tex}} |$}} {{math| {{norm|''x''}} |&&}} || x ||{{math| {{norm|''x''|tex}} |$$}}
Examples with numerical evaluation
Code Result {{math| {{norm|{{op|-}}6}} {{=}} {{norm|{{op|-}}6|#}} |&}} || − 6 ||= 6{{math| {{norm|{{op|-}}6.5}} {{=}} {{norm|{{op|-}}6.5|#}} |&}} || − 6.5 ||= 6.5{{math| {{norm|6.5}} {{=}} {{norm|6.5|#}} |&}} || 6.5 ||= 6.5{{math| {{norm|{{op|+}}6}} {{=}} {{norm|{{op|+}}6|#}} |&}} || + 6 ||= 6{{math| {{norm|0}} {{=}} {{norm|0|#}} |&}} || 0 ||= 0{{math| {{norm|{{op|-}}6.5e+45}} {{=}} {{norm|{{op|-}}6.5e+45|#}} |&}} || − 6.5e+45 ||= 6.5E+45{{math| {{norm|{{op|-}}6E-12}} {{=}} {{norm|{{op|-}}6E-12|#}} |&}} || − 6E-12 ||= 6.0E − 12{{math| {{norm|{{op|-}}6E{{op|-}}12}} {{=}} {{norm|{{op|-}}6E{{op|-}}12|#}} |&}} || − 6E − 12 ||= 6.0E − 12{{math| {{norm|6,500}} {{=}} {{norm|{{formatnum: 6,500|R}}|#}} |&}} || 6,500 ||= 6500{{math| {{norm|3; 4}} {{=}} {{norm|3; 4|#}} |&}} || 3; 4 ||= 5{{math| {{norm|{{op|-}}3; {{op|-}}4}} {{=}} {{norm|{{op|-}}3; {{op|-}}4|#}} |&}} || − 3; − 4 ||= 5{{math| {{norm|1; 1}} {{=}} {{norm|1; 1|#}} |&}} || 1; 1 ||= 1.4142135623731{{math| {{norm|{{op|-}}3; {{op|-}}4; 1}} {{=}} {{norm|{{op|-}}3; {{op|-}}4; 1|#}} |&}} || − 3; − 4; 1 ||= 5.0990195135928{{math| {{norm|{{op|-}}3; {{op|-}}4; 1; 1}} {{=}} {{norm|{{op|-}}3; {{op|-}}4; 1; 1|#}} |&}} || − 3; − 4; 1; 1 ||= 5.1961524227066{{math| {{norm|3; 4|3}} {{=}} {{norm|3; 4|3|#}} |&}} || 3; 4 ||3 = 4.4979414452754{{math| {{norm|{{op|-}}6}} {{=}} {{norm|{{op|-}}6|#}} |&}} || − 6 ||= 6{{math| {{norm|{{op|-|tex}}6|tex}} {{=}} {{norm|{{op|-|tex}}6|#}} |$}} {{math| {{norm|{{op|-}}6}} {{=}} {{norm|{{op|-}}6|#}} |&&}} || −6 ||= 6{{math| {{norm|{{op|-|tex}}6|tex}} {{=}} {{norm|{{op|-|tex}}6|#}} |$$}} {{math| {{norm|3; 4}} {{=}} {{norm|3; 4|#}} |&&}} || 3; 4 ||= 5{{math| {{norm|3; 4|tex}} {{=}} {{norm|3; 4|#}} |$$}} {{math| {{norm|{{op|-}}3; {{op|-}}4|HTM}} {{=}} {{norm|{{op|-}}3; {{op|-}}4|#}} |&}} = 5− 3; − 4 {{math| {{norm|{{op|-}}3; {{op|-}}4|TEX}} {{=}} {{norm|{{op|-}}3; {{op|-}}4|#}} |$}} {{math| {{norm|1; 1}} {{=}} {{norm|1; 1|#}} |&}} || 1; 1 ||= 1.4142135623731{{math| {{norm|1; 1|tex}} {{=}} {{norm|1; 1|#}} |$}} {{math| {{norm|{{op|-}}3; {{op|-}}4; 1}} {{=}} {{norm|{{op|-}}3; {{op|-}}4; 1|#}} |&&}} || −3; −4; 1 ||= 5.0990195135928{{math| {{norm|{{op|-}}3; {{op|-}}4; 1|tex}} {{=}} {{norm|{{op|-}}3; {{op|-}}4; 1|#}} |$$}} {{math| {{norm|{{op|-}}3; {{op|-}}4; 1; 1|HTM}} {{=}} {{norm|{{op|-}}3; {{op|-}}4; 1; 1|#}} |&}} = 5.1961524227066− 3; − 4; 1; 1 {{math| {{norm|{{op|-}}3; {{op|-}}4; 1; 1|TEX}} {{=}} {{norm|{{op|-}}3; {{op|-}}4; 1; 1|#}} |$}} {{math| {{norm|3; 4|3|HTM}} {{=}} {{norm|3; 4|3|#}} |&&}} = 4.4979414452754
33; 4 {{math| {{norm|3; 4|3|TEX}} {{=}} {{norm|3; 4|3|#}} |$$}}
More elaborate examples
The code
- {{math| ''x''{{^|3}} {{op|-}} ''x''{{^|2}} {{op|+}} 1 |&&}}, {{math| ''x''{{^|3|tex}} {{op|-|tex}} ''x''{{^|2|tex}} {{op|+|tex}} 1 |$$}}
yields the HTML+CSS formatted, LaTeX formatted
- ,
x 3 − x 2 + 1
while the code
- {{math| ''x''{{^|3}} {{op|-}} ''x''{{^|2}} {{op|+}} 1 |&}}, {{math| ''x''{{^|3|tex}} {{op|-|tex}} ''x''{{^|2|tex}} {{op|+|tex}} 1 |$}}
yields the HTML+CSS formatted, LaTeX formatted
-
,x 3 − x 2 + 1
The code
- {{math| {{norm| ''x''{{^|3}} {{op|-}} ''x''{{^|2}} {{op|+}} 1 |HTM}} |&&}}, {{math| {{norm| ''x''{{^|3|tex}} {{op|-|tex}} ''x''{{^|2|tex}} {{op|+|tex}} 1 |TEX}} |$$}}
yields the HTML+CSS formatted, LaTeX formatted
- ,
x 3 − x 2 + 1
while the code
- {{math| {{norm| ''x''{{^|3}} {{op|-}} ''x''{{^|2}} {{op|+}} 1 |HTM}} |&}}, {{math| {{norm| ''x''{{^|3|tex}} {{op|-|tex}} ''x''{{^|2|tex}} {{op|+|tex}} 1 |TEX}} |$}}
yields the HTML+CSS formatted, LaTeX formatted
-
,x 3 − x 2 + 1
The code
- {{math| {{norm| {{frac| 1 | ''x''{{^|3}} {{op|-}} ''x''{{^|2}} {{op|+}} 1 |HTM}} |HTM}} |&&}}, {{math| {{norm| {{frac| 1 | ''x''{{^|3|tex}} {{op|-|tex}} ''x''{{^|2|tex}} {{op|+|tex}} 1 |TEX}} |TEX}} |$$}}
yields the HTML+CSS formatted, LaTeX formatted
- ,
1 x 3 − x 2 + 1
while the code
- {{math| {{norm| {{frac| 1 | ''x''{{^|3}} {{op|-}} ''x''{{^|2}} {{op|+}} 1 |htm}} |HTM}} |&}}, {{math| {{norm| {{frac| 1 | ''x''{{^|3|tex}} {{op|-|tex}} ''x''{{^|2|tex}} {{op|+|tex}} 1 |tex}} |TEX}} |$}}
yields the HTML+CSS formatted, LaTeX formatted
-
,1 x 3 − x 2 + 1
Examples with invalid input
Code | Result | Comment |
---|---|---|
{{norm|#}} | Expression error: Unrecognized word "strong". | |
{{norm|6,500|#}} | Expression error: Unrecognized word "strong". | (formatted numbers are not allowed) |
{{norm|i|#}} | Expression error: Unrecognized word "strong". | |
{{norm|blob|#}} | Expression error: Unrecognized word "strong". | |
{{norm|6 blobs|#}} | Expression error: Unrecognized word "strong". |